Resonance vibrations of elastic waveguides with inertial inclusions

The problem of resonance oscillations of inertial inclusions in contact wit h elastic waveguides has triggered a number of theoretical investigations. It was shown [1-3] that related phenomena may be treated by solving the spe ctral problem posed for a differential equation that is defined in an infin itely long interval. For specific waveguide and inclusion parameters, a com posite system that includes interacting objects with lumped and distributed parameters may have a mixed (continuous and line) eigenfrequency spectrum. The line spectrum may be observed both before and after the boundary frequ ency. It was noted [3, 4] that the presence of an isolated lumped inertial element causes the line eigenfrequency spectrum, which extends to the bound ary frequency. So-called trap oscillations are responsible for this spectru m. However, little is yet known about these effects, which hinders their ef fective use in practice. First, conditions for trap oscillations should be generalized for the case of multielement inclusions in various infinite wav eguides. Second, the effect of edge conditions on the line spectrum in a se mi-infinite waveguide calls for in-depth investigation. The solution to the se problems would formulate proper ways of tackling engineering challenges associated with the interaction of a railway track with high-speed rolling stock [5]. Issues discussed in this paper are also concerned with object ch aracterization from analysis of its eigenfrequency spectrum. In recent year s, this technique has gained wide acceptance in crystallography and other f ields of science and technology as a promising tool for the acquisition and processing of data on the internal structure of an object. (C) 2000 MAIK " Nauka/Interperiodica".